Most linear algebra courses start by considering how to solve a system of linear equations. \[ \begin{align} a_{0,0}x_0 + a_{0,1}x_0 + \cdots a_{0,n-1}x_0 & = b_0 ...

Dr. James McCaffrey presents a complete end-to-end demonstration of linear regression using pseudo-inverse training. Compared to other training techniques, such as stochastic gradient descent, ...

Grade school math students are likely familiar with teachers admonishing them not to just guess the answer to a problem. But a new proof establishes that, in fact, the right kind of guessing is ...

Make sure you are confident in calculating with negative numbers, which is a skill often needed to solve equations. To solve the equation, do the inverse operation. The inverse of multiplying by 12 is ...

Dr. James McCaffrey of Microsoft Research presents a full-code, step-by-step tutorial on an implementation of the technique that emphasizes simplicity and ease-of-modification over robustness and ...

Solve the equation \(\frac{3s + 9}{4} = 7\). This means \(3s + 9\) has all been divided by 4. To solve the equation, inverse the operations. The opposite of dividing by 4 is multiplying by 4. Any ...